On exact infinity-categories and the Theorem of the Heart

Abstract

We introduce a notion of exact quasicategory, and we prove an analogue of Amnon Neeman's Theorem of the Heart for Waldhausen K-theory.

27 pages. Repaired botched proof of the main theorem

References in corpus (3)

• Higher Topos Theory
• The localization sequence for the algebraic K-theory of topological K-theory
• Regularity of structured ring spectra and localization in K-theory

Cited by in corpus (27)

• On the Q construction for exact quasicategories
• External triangulation of the homotopy category of exact quasi-category
• K-theory and G-theory of derived algebraic stacks
• Motivic Realizations of Singularity Categories and Vanishing Cycles
• Regularity of structured ring spectra and localization in K-theory
• Exact structures and degeneration of Hall algebras
• Purity in chromatically localized algebraic $K$-theory
• Weight structures and the algebraic $K$-theory of stable $\infty$-categories
• The special fiber of the motivic deformation of the stable homotopy category is algebraic
• Positive and negative extensions in extriangulated categories
• A^1-homotopy invariance in spectral algebraic geometry
• K-theory of endomorphisms via noncommutative motives
• Integral Models for Spaces via the Higher Frobenius
• Dévissage for Waldhausen K-theory
• Determinant map for the prestack of Tate objects
• The universal Hall bialgebra of a double 2-Segal space
• Real K-theory for Waldhausen infinity categories with genuine duality
• The Fundamental Theorem of Localizing Invariants
• A categorification of the quantum Lefschetz principle
• From Six Functors Formalisms to Derived Motivic Measures
• Segal K-theory of vector spaces with an automorphism
• Categorifying rationalization
• Algebraic K-theory of finitely projective modules on ${\mathbb{E}}_{\infty }$-rings
• K-theory of semi-linear endomorphisms via the Riemann-Hilbert correspondence
• Integration of Voevodsky motives
• A dévissage theorem of non-connective $K$-theory
• On exact categories and their stable envelopes